Finite Group Databasebeta

← #15675045

Subgroups — #15675045

Order 2944.

266 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13092982C211yesmaximal, characteristic
2#13092398C211yesmaximal, characteristic, complemented
3#13092389C211yesmaximal, characteristic, complemented
4#13092205C211yesmaximal, characteristic, complemented
5#13092204C211yesmaximal, characteristic, complemented
6#13092203C211yesmaximal, characteristic, complemented
7C23×AΣL(1,𝔽16)C211yesmaximal, characteristic, complemented
8C22×C22⋊D23C411yescharacteristic, complemented
9C2×#67290C2211yescharacteristic
10C23×#120C2211yescharacteristic
11#10625124C411yescharacteristic, complemented
12#10625111—21no—
13#10625110—21no—
14#10625108C2211yescharacteristic
15M16×D23—21no—
16#10625056—21no—
17#10625055—21no—
18#10625053C411yescharacteristic, complemented
19#10625048—21no—
20#10625048C411yescharacteristic, complemented
21C23×#100C2211yescharacteristic
22C23×#99C2211yescharacteristic
23#10625016C2211yescharacteristic
24#10625015C2211yescharacteristic
25#10625006—21no—
26#10624988—21no—
27C24×C23C2×C411yescharacteristic
28C23×D23C2×C411yescharacteristic
29C2×D4×C23—21no—
30C2×D4×C23C2311yescharacteristic
31C2×C22⋊D23—21no—
32C2×C22⋊D23—21no—
33C2×C22⋊D23—21no—
34C2×C22⋊D23—21no—
35C2×C22⋊D23—41no—
36C2×C22⋊D23—41no—
37C2×C22⋊D23C2×C411yescharacteristic
38C2×C22⋊D23D411yescharacteristic
39C22×Dic23C2×C411yescharacteristic
40C22×Dic23D411yescharacteristic
41#67290—41no—
42#67290—41no—
43C2×D92—21no—
44C2×C4×D23D411yescharacteristic
45C2×Dic46D411yescharacteristic
46M16×C23—21no—
47C22⋊C4×C23—21no—
48C22⋊C4×C23—21no—
49C22⋊C4×C23C2×C411yescharacteristic
50C22⋊Dic23—21no—
51C22⋊Dic23—21no—
52C22⋊Dic23C2×C411yescharacteristic
53(C2×D23)⋊C4—21no—
54(C2×D23)⋊C4—21no—
55Dic23⋊C4—21no—
56Dic23⋊C4—41no—
57C4×Dic23—21no—
58C4×Dic23—41no—
59#67267—21no—
60#67262—41no—
61C8×D23—41no—
62C23×C23—21no—
63C23×C23—41no—
64C23×C23—81no—
65C23×C23C22×C411yescharacteristic
66C23×C23C2×D411yescharacteristic
67C22×D23—21no—
68C22×D23—41no—
69C22×D23—81no—
70C22×D23C22⋊C411yescharacteristic
71D4×C23—41no—
72D4×C23—81no—
73C2×C4×C23—21no—
74C2×C4×C23—41no—
75C2×C4×C23C2×D411yescharacteristic
76C22⋊D23—41no—
77C22⋊D23—41no—
78C22⋊D23—42no—
79C22⋊D23—41no—
80C22⋊D23—41no—
81C22⋊D23—81no—
82C22⋊D23—81no—
83C2×Dic23—21no—
84C2×Dic23—21no—
85C2×Dic23—21no—
86C2×Dic23—21no—
87C2×Dic23—21no—
88C2×Dic23—41no—
89C2×Dic23C22⋊C411yescharacteristic
90C2×Dic23C22⋊C411yescharacteristic
91C2×Dic23C22⋊C411yescharacteristic
92D92—81no—
93C4×D23—21no—
94C4×D23—21no—
95Dic46—41no—
96C8×C23—41no—
97C23⋊C8—41no—
98#2122—231nomaximal, Sylow
99C22×C23—21no—
100C22×C23—21no—
101C22×C23—41no—
102C22×C23—41no—
103C22×C23—41no—
104C22×C23—41no—
105C22×C23—41no—
106C22×C23—82no—
107C22×C23C2×C22⋊C411yescharacteristic
108C2×D23—21no—
109C2×D23—41no—
110C2×D23—41no—
111C2×D23—41no—
112C2×D23—41no—
113C2×D23—82no—
114C4×C23—21no—
115C4×C23—41no—
116C4×C23—81no—
117Dic23—21no—
118Dic23—21no—
119Dic23—41no—
120Dic23—81no—
121Dic23#9911yescharacteristic
122Dic23#9911yescharacteristic
123#535—231no—
124#413—231no—
125#410—231no—
126AΣL(1,𝔽16)—231no—
127AΣL(1,𝔽16)—231no—
128AΣL(1,𝔽16)—231no—
129AΣL(1,𝔽16)D2311yescharacteristic, complemented
130C2×C23—21no—
131C2×C23—41no—
132C2×C23—41no—
133C2×C23—81no—
134C2×C23C2×#9911yescharacteristic
135D23—41no—
136D23—81no—
137C2×#41—231no—
138C22×D4—231no—
139C2×M16—461no—
140#127—461no—
141#124—461no—
142#121—461no—
143#121—461no—
144#120—231no—
145#120—231no—
146#120—231no—
147#120C2×D2311yescharacteristic
148#117—231no—
149#117—461no—
150#101—461no—
151#100—231no—
152#100C2×D2311yescharacteristic
153#99—231no—
154#99—461no—
155#99C2×D2311yescharacteristic
156C23#212211yescharacteristic, complemented, Sylow
157C24—231no—
158C24C4×D2311yescharacteristic
159#41—921no—
160#41—921no—
161C2×Q8—231no—
162C2×D4—21no—
163C2×D4—231no—
164C2×D4—231no—
165C2×D4—461no—
166C2×D4—461no—
167C2×D4—461no—
168C2×D4—461no—
169C2×D4—461no—
170C2×D4—921no—
171C2×D4—921no—
172C2×D4C22×D2311yescharacteristic
173C22×C4—231no—
174C22×C4—231no—
175C22×C4—231no—
176M16—21no—
177M16—461no—
178M16—921no—
179C2×C8—921no—
180C4⋊C4—461no—
181C4⋊C4—921no—
182C22⋊C4—21no—
183C22⋊C4—21no—
184C22⋊C4—231no—
185C22⋊C4—461no—
186C22⋊C4—461no—
187C22⋊C4—461no—
188C22⋊C4—461no—
189C22⋊C4C4×D2311yescharacteristic
190C42—461no—
191C42—921no—
192C23—21no—
193C23—41no—
194C23—81no—
195C23—231no—
196C23—461no—
197C23—921no—
198C23—1841no—
199C23C2×C4×D2311yescharacteristic
200C23D4×D2311yescharacteristic
201Q8—921no—
202D4—41no—
203D4—81no—
204D4—921no—
205D4—921no—
206D4—921no—
207D4—921no—
208D4—922no—
209D4—1841no—
210D4—1841no—
211D4—1841no—
212C2×C4—21no—
213C2×C4—41no—
214C2×C4—231no—
215C2×C4—231no—
216C2×C4—231no—
217C2×C4—461no—
218C2×C4—461no—
219C2×C4—461no—
220C2×C4—461no—
221C2×C4—461no—
222C2×C4—461no—
223C2×C4—461no—
224C2×C4—921no—
225C2×C4D4×D2311yescharacteristic
226C8—41no—
227C8—921no—
228C22—21no—
229C22—21no—
230C22—41no—
231C22—41no—
232C22—41no—
233C22—41no—
234C22—41no—
235C22—82no—
236C22—461no—
237C22—921no—
238C22—921no—
239C22—921no—
240C22—921no—
241C22—1842no—
242C22C22⋊C4×D2311yescharacteristic
243C4—21no—
244C4—41no—
245C4—81no—
246C4—231no—
247C4—231no—
248C4—461no—
249C4—461no—
250C4—921no—
251C4—1841no—
252C2—21no—
253C2—41no—
254C2—41no—
255C2—81no—
256C2—921no—
257C2—1841no—
258C2#99×D2311yescharacteristic
subgroupG/H
centerC2#99×D23
commutatorC23×C23C22×C4
FrattiniC2×D4C22×D23
FittingC23×AΣL(1,𝔽16)C2
socleC2×C23C2×#99
prime radical#13092982C2
cosocleC2×D4×C23C23
hypercenterAΣL(1,𝔽16)D23
hypocenterC23#2122
LCSG ▷ C23×C23 ▷ C22×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ AΣL(1,𝔽16)

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #13092398C2semidirect
3. #13092389C2semidirect
4. #13092205C2semidirect
5. #13092204C2semidirect
6. #13092203C2semidirect
7. C23×AΣL(1,𝔽16)C2semidirect
8. C22×C22⋊D23C4semidirect
11. #10625124C4semidirect
18. #10625053C4semidirect
20. #10625048C4semidirect
129. AΣL(1,𝔽16)D23semidirect
156. C23#2122semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#130929822
#130923982
#130923892
#130922052
#130922042
#130922032
C23×AΣL(1,𝔽16)2
#212223